Summary of Chapter 5

1 A complex project may be broken down into a number of separate activities. The completion of an activity is described as an event.2 Some activities may only be started once other activities are completed. This information may be shown in a precedence table, sometimes called a dependence table.3 An activity network provides a visual representation of the information given in a precedence table which makes it easier to work with. The type of activity network used on this course is called an activity on arc network. In this type of network, the activities are represented by arcs and events are represented as nodes.4 Each event has an early event time and a late event time. The early event time is the earliest time at which all of the dependent events may be completed. The late event time is the latest time at which any of the dependent events may be completed without delaying the project. Early event times are calculated using a forward scan and late event times are calculated using a backward scan.5 An activity is described as a critical activity if any increase in its duration results in a corresponding increase in the duration of the whole project.6 A path from the source node to the sink node which entirely follows critical activities is called a critical path. A critical path is the longest path contained in the network. It is possible for a project to have more than one critical path, in which case the total project time is the same on each one.7 At each vertex on a critical path the early event time is equal to the late event time.8 The total float of an activity is the amount of time that its start may be delayed without affecting the duration of the project.   total float = latest finish time - duration - earliest start time.   The total float of any critical activity is zero.9 A cascade (Gantt) chart provides a graphical way to represent the range of possible start and finish times for all activities on a single diagram.10 A scheduling diagram is used to show how tasks are allocated to workers in order to complete a project subject to constraints on the time required or the number of workers available.11 In general, a lower bound for the number of workers needed to complete a project within its critical time is given by the smallest integer greater than or equal to    sum of all the activity times    ---------------------------------------    critical time of the project12 A dummy activity is shown by a dotted line. It has an arrow to indicate direction, but no weight.13 Dummies are needed for two reasons:  for example, if activity D depends only on activity B but activity E depends on activities B and C. to enable the unique representation of activities in therms of their end events.

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